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Sheaves in Geometry and Logic [[electronic resource] ] : A First Introduction to Topos Theory / / by Saunders MacLane, Ieke Moerdijk
| Sheaves in Geometry and Logic [[electronic resource] ] : A First Introduction to Topos Theory / / by Saunders MacLane, Ieke Moerdijk |
| Autore | MacLane Saunders |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (XII, 630 p.) |
| Disciplina | 512/.55 |
| Collana | Universitext |
| Soggetto topico |
Geometry
K-theory Mathematical logic K-Theory Mathematical Logic and Foundations |
| ISBN | 1-4612-0927-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Prologue -- Categorial Preliminaries -- I. Categories of Functors -- 1. The Categories at Issue -- 2. Pullbacks -- 3. Characteristic Functions of Subobjects -- 4. Typical Subobject Classifiers -- 5. Colimits -- 6. Exponentials -- 7. Propositional Calculus -- 8. Heyting Algebras -- 9. Quantifiers as Adjoints -- Exercises -- II. Sheaves of Sets -- 1. Sheaves -- 2. Sieves and Sheaves -- 3. Sheaves and Manifolds -- 4. Bundles -- 5. Sheaves and Cross-Sections -- 6. Sheaves as Étale Spaces -- 7. Sheaves with Algebraic Structure -- 8. Sheaves are Typical -- 9. Inverse Image Sheaf -- Exercises -- III. Grothendieck Topologies and Sheaves -- 1. Generalized Neighborhoods -- 2. Grothendieck Topologies -- 3. The Zariski Site -- 4. Sheaves on a Site -- 5. The Associated Sheaf Functor -- 6. First Properties of the Category of Sheaves -- 7. Subobject Classifiers for Sites -- 8. Subsheaves -- 9. Continuous Group Actions -- Exercises -- IV. First Properties of Elementary Topoi -- 1. Definition of a Topos -- 2. The Construction of Exponentials -- 3. Direct Image -- 4. Monads and Beck’s Theorem -- 5. The Construction of Colimits -- 6. Factorization and Images -- 7. The Slice Category as a Topos -- 8. Lattice and Heyting Algebra Objects in a Topos -- 9. The Beck-Chevalley Condition -- 10. Injective Objects -- Exercises -- V. Basic Constructions of Topoi -- 1. Lawvere-Tierney Topologies -- 2. Sheaves -- 3. The Associated Sheaf Functor -- 4. Lawvere-Tierney Subsumes Grothendieck -- 5. Internal Versus External -- 6. Group Actions -- 7. Category Actions -- 8. The Topos of Coalgebras -- 9. The Filter-Quotient Construction -- Exercises -- VI. Topoi and Logic -- 1. The Topos of Sets -- 2. The Cohen Topos -- 3. The Preservation of Cardinal Inequalities -- 4. The Axiom of Choice -- 5. The Mitchell-Bénabou Language -- 6. Kripke-Joyal Semantics -- 7. Sheaf Semantics -- 8. Real Numbers in a Topos -- 9. Brouwer’s Theorem: All Functions are Continuous -- 10. Topos-Theoretic and Set-Theoretic Foundations -- Exercises -- VII. Geometric Morphisms -- 1. Geometric Morphisms and Basic Examples -- 2. Tensor Products -- 3. Group Actions -- 4. Embeddings and Surjections -- 5. Points -- 6. Filtering Functors -- 7. Morphisms into Grothendieck Topoi -- 8. Filtering Functors into a Topos -- 9. Geometric Morphisms as Filtering Functors -- 10. Morphisms Between Sites -- Exercises -- VIII. Classifying Topoi -- 1. Classifying Spaces in Topology -- 2. Torsors -- 3. Classifying Topoi -- 4. The Object Classifier -- 5. The Classifying Topos for Rings -- 6. The Zariski Topos Classifies Local Rings -- 7. Simplicial Sets -- 8. Simplicial Sets Classify Linear Orders -- Exercises -- IX. Localic Topoi -- 1. Locales -- 2. Points and Sober Spaces -- 3. Spaces from Locales -- 4. Embeddings and Surjections of Locales -- 5. Localic Topoi -- 6. Open Geometric Morphisms -- 7. Open Maps of Locales -- 8. Open Maps and Sites -- 9. The Diaconescu Cover and Barr’s Theorem -- 10. The Stone Space of a Complete Boolean Algebra -- 11. Deligne’s Theorem -- Exercises -- X. Geometric Logic and Classifying Topoi -- 1. First-Order Theories -- 2. Models in Topoi -- 3. Geometric Theories -- 4. Categories of Definable Objects -- 5. Syntactic Sites -- 6. The Classifying Topos of a Geometric Theory -- 7. Universal Models -- Exercises -- Appendix: Sites for Topoi -- Epilogue -- Index of Notation. |
| Record Nr. | UNINA-9910480323003321 |
MacLane Saunders
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Sheaves in Geometry and Logic [[electronic resource] ] : A First Introduction to Topos Theory / / by Saunders MacLane, Ieke Moerdijk
| Sheaves in Geometry and Logic [[electronic resource] ] : A First Introduction to Topos Theory / / by Saunders MacLane, Ieke Moerdijk |
| Autore | MacLane Saunders |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (XII, 630 p.) |
| Disciplina | 512/.55 |
| Collana | Universitext |
| Soggetto topico |
Geometry
K-theory Mathematical logic K-Theory Mathematical Logic and Foundations |
| ISBN | 1-4612-0927-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Prologue -- Categorial Preliminaries -- I. Categories of Functors -- 1. The Categories at Issue -- 2. Pullbacks -- 3. Characteristic Functions of Subobjects -- 4. Typical Subobject Classifiers -- 5. Colimits -- 6. Exponentials -- 7. Propositional Calculus -- 8. Heyting Algebras -- 9. Quantifiers as Adjoints -- Exercises -- II. Sheaves of Sets -- 1. Sheaves -- 2. Sieves and Sheaves -- 3. Sheaves and Manifolds -- 4. Bundles -- 5. Sheaves and Cross-Sections -- 6. Sheaves as Étale Spaces -- 7. Sheaves with Algebraic Structure -- 8. Sheaves are Typical -- 9. Inverse Image Sheaf -- Exercises -- III. Grothendieck Topologies and Sheaves -- 1. Generalized Neighborhoods -- 2. Grothendieck Topologies -- 3. The Zariski Site -- 4. Sheaves on a Site -- 5. The Associated Sheaf Functor -- 6. First Properties of the Category of Sheaves -- 7. Subobject Classifiers for Sites -- 8. Subsheaves -- 9. Continuous Group Actions -- Exercises -- IV. First Properties of Elementary Topoi -- 1. Definition of a Topos -- 2. The Construction of Exponentials -- 3. Direct Image -- 4. Monads and Beck’s Theorem -- 5. The Construction of Colimits -- 6. Factorization and Images -- 7. The Slice Category as a Topos -- 8. Lattice and Heyting Algebra Objects in a Topos -- 9. The Beck-Chevalley Condition -- 10. Injective Objects -- Exercises -- V. Basic Constructions of Topoi -- 1. Lawvere-Tierney Topologies -- 2. Sheaves -- 3. The Associated Sheaf Functor -- 4. Lawvere-Tierney Subsumes Grothendieck -- 5. Internal Versus External -- 6. Group Actions -- 7. Category Actions -- 8. The Topos of Coalgebras -- 9. The Filter-Quotient Construction -- Exercises -- VI. Topoi and Logic -- 1. The Topos of Sets -- 2. The Cohen Topos -- 3. The Preservation of Cardinal Inequalities -- 4. The Axiom of Choice -- 5. The Mitchell-Bénabou Language -- 6. Kripke-Joyal Semantics -- 7. Sheaf Semantics -- 8. Real Numbers in a Topos -- 9. Brouwer’s Theorem: All Functions are Continuous -- 10. Topos-Theoretic and Set-Theoretic Foundations -- Exercises -- VII. Geometric Morphisms -- 1. Geometric Morphisms and Basic Examples -- 2. Tensor Products -- 3. Group Actions -- 4. Embeddings and Surjections -- 5. Points -- 6. Filtering Functors -- 7. Morphisms into Grothendieck Topoi -- 8. Filtering Functors into a Topos -- 9. Geometric Morphisms as Filtering Functors -- 10. Morphisms Between Sites -- Exercises -- VIII. Classifying Topoi -- 1. Classifying Spaces in Topology -- 2. Torsors -- 3. Classifying Topoi -- 4. The Object Classifier -- 5. The Classifying Topos for Rings -- 6. The Zariski Topos Classifies Local Rings -- 7. Simplicial Sets -- 8. Simplicial Sets Classify Linear Orders -- Exercises -- IX. Localic Topoi -- 1. Locales -- 2. Points and Sober Spaces -- 3. Spaces from Locales -- 4. Embeddings and Surjections of Locales -- 5. Localic Topoi -- 6. Open Geometric Morphisms -- 7. Open Maps of Locales -- 8. Open Maps and Sites -- 9. The Diaconescu Cover and Barr’s Theorem -- 10. The Stone Space of a Complete Boolean Algebra -- 11. Deligne’s Theorem -- Exercises -- X. Geometric Logic and Classifying Topoi -- 1. First-Order Theories -- 2. Models in Topoi -- 3. Geometric Theories -- 4. Categories of Definable Objects -- 5. Syntactic Sites -- 6. The Classifying Topos of a Geometric Theory -- 7. Universal Models -- Exercises -- Appendix: Sites for Topoi -- Epilogue -- Index of Notation. |
| Record Nr. | UNINA-9910789344003321 |
|
MacLane Saunders
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Sheaves in Geometry and Logic [[electronic resource] ] : A First Introduction to Topos Theory / / by Saunders MacLane, Ieke Moerdijk
| Sheaves in Geometry and Logic [[electronic resource] ] : A First Introduction to Topos Theory / / by Saunders MacLane, Ieke Moerdijk |
| Autore | MacLane Saunders |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (XII, 630 p.) |
| Disciplina | 512/.55 |
| Collana | Universitext |
| Soggetto topico |
Geometry
K-theory Mathematical logic K-Theory Mathematical Logic and Foundations |
| ISBN | 1-4612-0927-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Prologue -- Categorial Preliminaries -- I. Categories of Functors -- 1. The Categories at Issue -- 2. Pullbacks -- 3. Characteristic Functions of Subobjects -- 4. Typical Subobject Classifiers -- 5. Colimits -- 6. Exponentials -- 7. Propositional Calculus -- 8. Heyting Algebras -- 9. Quantifiers as Adjoints -- Exercises -- II. Sheaves of Sets -- 1. Sheaves -- 2. Sieves and Sheaves -- 3. Sheaves and Manifolds -- 4. Bundles -- 5. Sheaves and Cross-Sections -- 6. Sheaves as Étale Spaces -- 7. Sheaves with Algebraic Structure -- 8. Sheaves are Typical -- 9. Inverse Image Sheaf -- Exercises -- III. Grothendieck Topologies and Sheaves -- 1. Generalized Neighborhoods -- 2. Grothendieck Topologies -- 3. The Zariski Site -- 4. Sheaves on a Site -- 5. The Associated Sheaf Functor -- 6. First Properties of the Category of Sheaves -- 7. Subobject Classifiers for Sites -- 8. Subsheaves -- 9. Continuous Group Actions -- Exercises -- IV. First Properties of Elementary Topoi -- 1. Definition of a Topos -- 2. The Construction of Exponentials -- 3. Direct Image -- 4. Monads and Beck’s Theorem -- 5. The Construction of Colimits -- 6. Factorization and Images -- 7. The Slice Category as a Topos -- 8. Lattice and Heyting Algebra Objects in a Topos -- 9. The Beck-Chevalley Condition -- 10. Injective Objects -- Exercises -- V. Basic Constructions of Topoi -- 1. Lawvere-Tierney Topologies -- 2. Sheaves -- 3. The Associated Sheaf Functor -- 4. Lawvere-Tierney Subsumes Grothendieck -- 5. Internal Versus External -- 6. Group Actions -- 7. Category Actions -- 8. The Topos of Coalgebras -- 9. The Filter-Quotient Construction -- Exercises -- VI. Topoi and Logic -- 1. The Topos of Sets -- 2. The Cohen Topos -- 3. The Preservation of Cardinal Inequalities -- 4. The Axiom of Choice -- 5. The Mitchell-Bénabou Language -- 6. Kripke-Joyal Semantics -- 7. Sheaf Semantics -- 8. Real Numbers in a Topos -- 9. Brouwer’s Theorem: All Functions are Continuous -- 10. Topos-Theoretic and Set-Theoretic Foundations -- Exercises -- VII. Geometric Morphisms -- 1. Geometric Morphisms and Basic Examples -- 2. Tensor Products -- 3. Group Actions -- 4. Embeddings and Surjections -- 5. Points -- 6. Filtering Functors -- 7. Morphisms into Grothendieck Topoi -- 8. Filtering Functors into a Topos -- 9. Geometric Morphisms as Filtering Functors -- 10. Morphisms Between Sites -- Exercises -- VIII. Classifying Topoi -- 1. Classifying Spaces in Topology -- 2. Torsors -- 3. Classifying Topoi -- 4. The Object Classifier -- 5. The Classifying Topos for Rings -- 6. The Zariski Topos Classifies Local Rings -- 7. Simplicial Sets -- 8. Simplicial Sets Classify Linear Orders -- Exercises -- IX. Localic Topoi -- 1. Locales -- 2. Points and Sober Spaces -- 3. Spaces from Locales -- 4. Embeddings and Surjections of Locales -- 5. Localic Topoi -- 6. Open Geometric Morphisms -- 7. Open Maps of Locales -- 8. Open Maps and Sites -- 9. The Diaconescu Cover and Barr’s Theorem -- 10. The Stone Space of a Complete Boolean Algebra -- 11. Deligne’s Theorem -- Exercises -- X. Geometric Logic and Classifying Topoi -- 1. First-Order Theories -- 2. Models in Topoi -- 3. Geometric Theories -- 4. Categories of Definable Objects -- 5. Syntactic Sites -- 6. The Classifying Topos of a Geometric Theory -- 7. Universal Models -- Exercises -- Appendix: Sites for Topoi -- Epilogue -- Index of Notation. |
| Record Nr. | UNINA-9910812418703321 |
|
MacLane Saunders
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Simplicial and dendroidal homotopy theory / / Gijs Heuts, Ieke Moerdijk
| Simplicial and dendroidal homotopy theory / / Gijs Heuts, Ieke Moerdijk |
| Autore | Heuts Gijs |
| Pubbl/distr/stampa | Cham, : Springer Nature, 2022 |
| Descrizione fisica | 1 online resource (xx, 612 pages) : illustrations |
| Altri autori (Persone) | MoerdijkIeke |
| Collana | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| Soggetto topico |
Homotopy theory
Teoria de l'homotopia |
| Soggetto genere / forma | Llibres electrònics |
| Soggetto non controllato |
Operads
infinity-operad infinity-category simplicial set dendroidal set simplicial space simplicial operad model categories Bousfield localization Boardman-Vogt higher algebra |
| ISBN | 3-031-10447-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I The Elementary Theory of Simplicial and Dendroidal Sets 1 Operads 2 Simplicial Sets 3 Dendroidal Sets 4 Tensor Products of Dendroidal Sets 5 Kan Conditions for Simplicial Sets 6 Kan Conditions for Dendroidal Sets Part II The Homotopy Theory of Simplicial and Dendroidal Sets 7 Model Categories 8 Model Structures on the Category of Simplicial Sets 9 Three Model Structures on the Category of Dendroidal Sets Part III The Homotopy Theory of Simplicial and Dendroidal Spaces 10 Reedy Categories and Diagrams of Spaces 11 Mapping Spaces and Bousfield Localizations 12 Dendroidal Spaces and ∞-Operads 13 Left Fibrations and the Covariant Model Structure 14 Simplicial Operads and ∞-Operads Epilogue References Index |
| Record Nr. | UNINA-9910586579203321 |
|
Heuts Gijs
|
||
| Cham, : Springer Nature, 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Simplicial and dendroidal homotopy theory / / Gijs Heuts, Ieke Moerdijk
| Simplicial and dendroidal homotopy theory / / Gijs Heuts, Ieke Moerdijk |
| Autore | Heuts Gijs |
| Pubbl/distr/stampa | Cham, : Springer Nature, 2022 |
| Descrizione fisica | 1 online resource (xx, 612 pages) : illustrations |
| Altri autori (Persone) | MoerdijkIeke |
| Collana | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| Soggetto topico |
Homotopy theory
Teoria de l'homotopia |
| Soggetto genere / forma | Llibres electrònics |
| Soggetto non controllato |
Operads
infinity-operad infinity-category simplicial set dendroidal set simplicial space simplicial operad model categories Bousfield localization Boardman-Vogt higher algebra |
| ISBN | 3-031-10447-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I The Elementary Theory of Simplicial and Dendroidal Sets 1 Operads 2 Simplicial Sets 3 Dendroidal Sets 4 Tensor Products of Dendroidal Sets 5 Kan Conditions for Simplicial Sets 6 Kan Conditions for Dendroidal Sets Part II The Homotopy Theory of Simplicial and Dendroidal Sets 7 Model Categories 8 Model Structures on the Category of Simplicial Sets 9 Three Model Structures on the Category of Dendroidal Sets Part III The Homotopy Theory of Simplicial and Dendroidal Spaces 10 Reedy Categories and Diagrams of Spaces 11 Mapping Spaces and Bousfield Localizations 12 Dendroidal Spaces and ∞-Operads 13 Left Fibrations and the Covariant Model Structure 14 Simplicial Operads and ∞-Operads Epilogue References Index |
| Record Nr. | UNISA-996485661003316 |
|
Heuts Gijs
|
||
| Cham, : Springer Nature, 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||